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        <title>API docs for &ldquo;sympy.integrals.integrals&rdquo;</title>
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        <body><h1 class="module">Module s.i.integrals</h1><span id="part">Part of <a href="sympy.integrals.html">sympy.integrals</a></span><div class="toplevel"><div class="undocumented">Undocumented</div></div><table class="children"><tr class="class"><td>Class</td><td><a href="sympy.integrals.integrals.Integral.html">Integral</a></td><td><div><p>Represents unevaluated integral.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.integrals.integrals.integrate">integrate</a></td><td><div><p>integrate(f, var, ...)</p>
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            <div class="functionHeader">def <a name="sympy.integrals.integrals.integrate">integrate(*args, **kwargs):</a></div>
            <div class="functionBody"><pre>integrate(f, var, ...)

Compute definite or indefinite integral of one or more variables
using Risch-Norman algorithm and table lookup. This procedure is
able to handle elementary algebraic and transcendental functions
and also a huge class of special functions, including Airy,
Bessel, Whittaker and Lambert.

var can be:

- a symbol                   -- indefinite integration
- a tuple (symbol, a, b)     -- definite integration

Several variables can be specified, in which case the result is multiple
integration.

Also, if no var is specified at all, then full-antiderivative of f is
returned. This is equivalent of integrating f over all it's variables.

Examples
--------

>>> from sympy import *
>>> x, y = symbols('xy')

>>> integrate(x*y, x)
(1/2)*y*x**2

>>> integrate(log(x), x)
-x + x*log(x)

>>> integrate(x)
(1/2)*x**2

>>> integrate(x*y)
(1/4)*x**2*y**2

See also the doctest of Integral._eval_integral(), which explains
thoroughly the strategy that SymPy uses for integration.</pre></div>
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